Galaxy S3 L710 Broken Screen and USB Debugging Not enabled

I have a completely stock Galaxy S3 L710 and the LCD/ Digitizer is broken and Black.
All other functions work on the phone.
I need to back everything up before replacing the LCD but USB Debugging is not enabled and ADB commands will not work since any commands require debugging enabled.

1) Is there a way to do a full system, app and file backup using adb commands?
2) Is it possible to enable USB Debugging via methods using adb commands?

Bob,
How do you know that the digitizer is broken and not just the LCD? For example, if you have someone call the phone and do the normal swipe to answer the call, does it fail to respond?

Sounds like a Catch-22 in regards to ADB and USB Debugging - you can't use ADB to turn on USB Debugging without USB Debugging on first.

You should be able to use the Kies software on your PC to backup things like Contacts, Call Logs, SMS/MMS, pictures/videos and your TouchWiz settings. However it will not backup your applications or app data. That shouldn't be a big deal, though, since even if you nuke the phone the Google Play Store will reload the apps (although not the data) after you login.

If you have an MHL<>HDMI adapter you can mirror the display on your TV. I don't know offhand if you can use a USB-ON-THE-GO adapter simultaneously so that you could use a USB mouse and keyboard for navigation.